In Exercises 1-4, write the simplex tableau for the given linear pro- gramming problem. (In each case the objective func

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In Exercises 1 4 Write The Simplex Tableau For The Given Linear Pro Gramming Problem In Each Case The Objective Func 1 (344.8 KiB) Viewed 15 times

In Exercises 1-4, write the simplex tableau for the given linear pro- gramming problem. (In each case the objective function is to be maximized.) 1. Objective function: 2. Objective function: :=x + 2x, :=x + 3x, Constraints: Constraints: 2x + x2=8 x + x = 4 x + x 55 XX1 X, X, 20 XX, 20 3. Objective function: 4. Objective function: : = 2x + 3x + 4x : = 6x - 9x; Constraints: Constraints: x + 2x, s 12 2x - 3x = 6 + xy S8 *, + X, 520 *, *xx, 20 In Exercises 5-8, explain why the linear programming problem is nor in standard form as given. 5. (Minimize) 6. (Maximize) Objective function: Objective function: :=x + x2 :=x + x2 Constraints: Constraints: x + 2x, 54 x + 2x, 5 6 X, X,20 2x, - XS-1 0 ܐܕܐ ܨ 11. Objective function: 12. Objective function: = = 5x + 2xy + 8x3 : = x - x + 2x Constraints: Constraints: 2x - 4x + x3 = 42 2x + 2x, 58 2x + 3x2 - xy = 42 X 55 6x,- X: + 3x, S 42 X, X, X, 20 X. X,X > 0 13. Objective function: 14. Objective function: : = 4x + 5x2 : = x + 2x Constraints: Constraints: x + x = 10 *, + 3x, s 15 3x + 7x, 42 2x - XS 12 X.X220 15. Objective function: 16. Objective function: : = 3x + 4x2 + x3 + 7x4 :X Constraints: Constraints: &x, + 3x2 + 4x3 + X57 3x + 2xy = 60 2x + 6x2 + x3 + 5x3 x + 2x, 28 x + 4x + 5xy + 2x, 58 x + 4x, 548 XX, X, X=0 *.X 0 18. Objective function: :=x - x + xy Solve : - 2x + xy + 3x3 Constraints: Constraints: this 2x + xy - 3x, S 40 x + xy + x, s 59 X + x3 = 25 one 2x + 3x75 2x + 3x, S 32 Q-15 X: + 6x 5 54 XX, X, 20 X, X, X30 19. Objective function: : = x + 2x2 - X4 Constraints: x + 2x + 3x3 24 3x2 + 7x3 + x = 42 XX, X3, XO 20. Objective function: : = x + 2x + xy - X4 Constraints: x + xy + 3x + 4x, S 60 X: + 2xy + 5.x, 550 2x + 3x3 + 6x, 72 X1, X3, X5, X620 0 ܕܐ.i + 7. (Maximize) 8. (Maximize) Objective function: Objective function: : = x + x Constraints: Constraints: x + xy + 3x, 55 x + x₂ Z4 2x -- 27,1 2x + x, 26 X2 + x 0 X, X, 20 X, X, X,20 In Exercises 9-20, use the simplex method to solve the given linear programming problem. (In each case the objective function is to be maximized.) 9. Objective function: 10. Objective function: :-*, + 2x = x + x3 Constraints: Constraints: x + 4x, 5 8 x + 2x, 6 3x + 2x, 512 *; 512 * X0 X, X, 20